The "rated capacity" printed on a battery is not a single fixed number. The faster you draw current, the less total charge it delivers. Adjust the rated capacity, Peukert exponent and discharge current to see the real runtime and capacity loss from Peukert's law update in real time.
The discharge-rate hours at which the rated capacity was measured
Actual discharge current I
A
The current at which the load actually discharges the battery
Results
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Rated discharge current (A)
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Effective capacity (this current) (Ah)
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Runtime (h)
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Ideal (k=1) runtime (h)
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Capacity utilisation (%)
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Capacity loss (Ah)
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Battery discharge — ideal vs Peukert
The battery charge level drains over time. The ideal (k=1) straight-line drain and the Peukert curve that empties sooner are overlaid; the gap between them is the capacity loss.
Runtime vs discharge current
Effective capacity vs discharge current
Theory & Key Formulas
$$t = H\left(\frac{C}{I\,H}\right)^{k}$$
Runtime t [h]. H is the rated discharge time, C the rated capacity [Ah], I the discharge current [A] and k the Peukert exponent (k = 1 for an ideal battery). A higher discharge current I gives a shorter runtime.
$$C_{\text{eff}} = I\,t, \qquad C_{\text{loss}} = C - C_{\text{eff}}$$
Effective capacity C_eff (the charge actually delivered at this current) and capacity loss C_loss (the capacity lost to the fast discharge).
Ideal runtime t_ideal (for a perfect k = 1 battery) and capacity utilisation η. The larger k is, the lower η becomes.
What is Peukert's Law?
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If a battery says "100 Ah", can't I just assume it lasts one hour at a 100-amp load?
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That is exactly the most common mistake. The rated capacity printed on a battery is not a single fixed number. How much energy you can actually draw out depends on how fast you draw it. The faster you discharge, the less total charge the battery delivers before it is flat. So that "100 Ah" figure is only honest when you discharge slowly.
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Wait — the same battery, but the capacity changes? Why does that happen?
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The reason is internal. At high discharge currents the chemical reactions cannot keep up uniformly throughout the electrodes, the internal resistance wastes more energy as heat, and the cell voltage sags to its cut-off point sooner. So a portion of the stored charge is simply left stranded deep inside the electrodes, unused when the discharge ends. Try raising the "discharge current I" on the left — you will see the runtime drop sharply.
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So Peukert's law is the formula that captures that "use it faster, lose more" behaviour.
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Right. In 1897 Wilhelm Peukert captured this with a compact empirical law. Its central parameter is the Peukert exponent k. A perfect, ideal battery would have k = 1, meaning its capacity does not depend on the discharge rate at all. But every real battery has k greater than 1. A good modern lithium-ion cell is close to ideal at around 1.05, a typical lead-acid battery is roughly 1.2 to 1.3, and an old, degraded battery is worse still. The larger k is, the more punishingly the usable capacity collapses as the load current rises.
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So when choosing a battery, I shouldn't just trust the nameplate capacity.
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Exactly. The rated capacity is only honest at the slow rated discharge rate it was measured at. Size a battery bank for a heavy, fast load using the nameplate capacity and you will get a runtime that is dramatically shorter than expected. Designers of electric vehicles, off-grid solar storage, UPS systems and marine house battery banks must always derate the nameplate capacity, using Peukert's law, for the actual load they intend to draw. Move the discharge-current slider on the charts below and you can clearly see that steep drop.
Frequently Asked Questions
Peukert's law is an empirical rule describing how the total charge a battery delivers (its effective capacity) shrinks the faster the battery is discharged. Its central parameter is the Peukert exponent k: an ideal battery has k=1 (capacity independent of discharge rate), while every real battery has k>1. A lithium-ion cell is around 1.05 and a lead-acid battery roughly 1.2-1.3; the larger k is, the more sharply the capacity collapses at high current. The runtime is runtime = H·(C/(I·H))^k, where C is the rated capacity, H the rated discharge time and I the discharge current.
At high discharge currents the chemical reactions cannot keep up uniformly throughout the electrodes, the internal resistance wastes more energy as heat, and the cell voltage sags to its cut-off point sooner. As a result, a portion of the stored charge is simply left stranded inside the electrodes and the discharge ends before it is used. Peukert's law captures this "the faster you use it, the more you lose" behaviour with a single exponent k.
The rated capacity (for example "100 Ah") is measured at the slow rated discharge rate, often a 20-hour rate. Size a battery bank for a heavy, fast load using this nameplate capacity and the runtime will be dramatically shorter than expected. Designers of electric vehicles, off-grid solar storage, UPS systems and marine house battery banks must always derate the nameplate capacity, using Peukert's law, for the actual load current they intend to draw.
An ideal battery has k=1. A good modern lithium-ion cell is close to ideal at around 1.05, a typical lead-acid battery is roughly 1.2 to 1.3, and an old or poor battery is worse still. The larger k is, the more punishingly the usable capacity collapses as the load current rises. This tool lets you vary k from 1.00 to 1.50, and you can confirm that with k=1 the runtime equals the ideal runtime.
Real-World Applications
Off-grid solar storage systems: In stand-alone power systems for homes or cabins, power is drawn from lead-acid or lithium-ion batteries at night or in cloudy weather. Lead-acid capacity is traditionally quoted at the 20-hour rate (C/20), but real loads often empty the battery in a few hours. If the effective capacity is not derated with Peukert's law, the power runs out in the middle of the night. The bank should be sized using the effective capacity at the expected peak discharge current.
UPS (uninterruptible power supply): A UPS in a server room or data centre supports the full load for only a short time — minutes to tens of minutes — during an outage. That is a very fast discharge, far from the 20-hour rate. UPS battery selection uses the manufacturer's high-rate discharge tables (5-minute, 15-minute rates) or a Peukert exponent to estimate the hold-up time. Sizing on the nameplate Ah alone can leave the system holding less than half the expected time when it matters most.
Electric vehicles and electric mobility: In EVs, electric forklifts and golf carts, large currents flow during every acceleration and climb. In a lead-acid electric forklift, shorter range on a heavy-duty work day is exactly the Peukert effect. Lithium-ion has k near 1.05, close to ideal, so the impact is small — yet at extreme high-rate discharge or low temperature it is not negligible. A guaranteed range requires capacity evaluation along the real-use discharge profile.
Marine house battery banks: The "house" battery on a yacht or boat supplies refrigerators, lighting, electronics and winches. A mix of continuous load while at anchor and brief high currents when using a winch makes Peukert-aware capacity sizing important. Some battery monitors apply a configured Peukert exponent to correct the displayed "time remaining", and the calculation in this tool helps make sense of how that works.
Common Misconceptions and Pitfalls
The biggest misconception is "the rated Ah is a single fixed performance figure for the battery". As you can see by moving k or the discharge current in this tool, the effective capacity you can draw from the same battery changes greatly with the discharge rate. The "100 Ah" number is only honest at the rated discharge time (such as the 20-hour rate); under any faster load the effective capacity drops. When reading a datasheet, always check at what hour-rate the capacity was measured. A capacity figure with no stated discharge rate is no basis for comparison.
Next, overconfidence that "Peukert's law applies universally to every battery". Peukert's law is an empirical rule that approximates the high-rate discharge of lead-acid batteries well, but for lithium-ion cells k is close to ideal at around 1.05 and the effect is comparatively small. The law also does not directly include the effect of temperature: in the cold the effective capacity drops further still, and as a battery degrades through cycling its effective k rises. The results of this tool are an estimate that assumes a room-temperature, healthy battery — in the field you must allow separately for a temperature correction and a degradation margin.
Finally, the misconception that "only the effective capacity matters; cut-off voltage and energy (Wh) can be ignored". Peukert's law deals with the charge delivered (Ah), not the energy (Wh) lost as the voltage falls during discharge. At high discharge currents the cell voltage itself sags, so the energy actually delivered shrinks even more than the Ah figure does. Furthermore, where you set the cut-off voltage also changes the runtime. In practice it is important to evaluate the voltage drop and energy balance alongside the Ah-based Peukert calculation.
How to Use
Enter battery rated capacity (Ah) in capNum field—typical lithium cells range 50–300 Ah, lead-acid 100–200 Ah
Set Peukert exponent (k) via kNum; standard values are k=1.1 for lithium, k=1.3 for lead-acid
Input desired discharge rate in hours (e.g., 5 for C/5 rate) or specify current (A) directly in curNum
Simulator calculates effective capacity at your discharge current, runtime accounting for nonlinear capacity loss, and compares ideal vs. actual performance
Worked Example
Lead-acid 200 Ah battery with k=1.25 discharged at 40 A (0.2 C rate): Rated capacity is 200 Ah at standard 20 A (C/20). At 40 A, Peukert's equation reduces effective capacity to approximately 185 Ah. Runtime = 185÷40 = 4.625 hours. Ideal runtime (k=1) would be 5 hours, revealing 7.5% capacity utilisation loss. If discharged at 80 A instead, effective capacity drops to 165 Ah, runtime becomes 2.06 hours versus ideal 2.5 hours—demonstrating how higher discharge currents amplify voltage sag and internal resistance effects typical in industrial UPS systems.
Practical Notes
Lead-acid automotive batteries show k≈1.35; marine deep-cycle k≈1.25; lithium LiFePO4 k≈1.05—always verify datasheet Peukert curve rather than assuming generic values
For critical systems (telecom, renewable backup), operate below 50% capacity utilisation to minimize efficiency loss and extend cycle life beyond 1000 cycles
Temperature correction: capacity loss accelerates 5–10% per 10°C below 25°C in lead-acid; adjust k upward for cold environments
Simultaneous high current + low temperature (e.g., 200 A from a 300 Ah pack at 0°C) can reduce effective capacity by 40%, making runtime predictions essential for mission-critical diesel generator switchover timing